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Jeremy, would you mind providing definitions for n, s and k?I checked. Only the divisors of 24 produce the specific symmetry such that:

s=(n-k^2)/(2k)

s+k =(n+k^2)/(2k)

(s+k)^2 - s^2 = n

**n**is clearly the automorphisms of the divisors of 24, but beyond that I am trying to decode in a precise way how you are getting your

**s**'s and

**k**'s.

Btw, in Lucas Sequence Notation where P = (s + k) and Q = (s * k) and D = P^2 - 4Q, the Discriminant, those 3 statements above can be reformulated, in order, via simple algebraic manipulation...

Q = (s * k) = ((n - k)^2)/(2)

P = (s + k) = ((n + k)^2)/(2k)

Q = (s * k) = ((n - k)^2)/(2)

sqrt (P^2 - 4Q), by the maths of Lucas Sequences, it follows, will always be an integer.

Also, could you clarify the below "claim" (as mathematicians call it) that "the square root produces the Klein four group from (n-k^2)/(2k)" (the first quoted mathematical statement above). What's apparent to you is not apparent to me. Don't forget that I'm self-taught too :-)

- ACSo one of the 4 Quantum "Spatial and angular momentum numbers" Ms where spin S = n-0.5

relative intensities = k(n+1-k)

http://en.wikipedia.org/wiki/Quantum_number#Spatial_and_angular_momentum_numbers

"the spin-raising operator is the square-root"

the square root produces the Klein four group from (n-k^2)/(2k)

P.S. As a little piece of mathematical trivia: D(P) = Q = 35 where P = (5 + 7) and Q = (5 * 7). What's the the next integer for which that relationship holds? Is it a common occurrence? Or an uncommon one?

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